Note on the optimality of (s,S)(s,S) policies for inventory systems with two demand classes

Sobel and Zhang [M.J. Sobel, Q.R. Zhang, Inventory Policies for Systems with Stochastic and Deterministic Demand, Operations Research 49 (1) (2001) 157–162] consider two periodic review inventory models with demand arriving simultaneously from a deterministic source and a random source. Under certain conditions, they show that an (s,S)(s,S) policy is optimal. For the first model, this note weakens one of their conditions while still obtaining the optimality of the (s,S)(s,S) policy. For the second model, this note shows that this condition can be removed entirely. The relaxation of the condition is helpful for extending the results of Sobel and Zhang to problems with fluctuating demand.